A reasercher collect samples of size N$=100$ and calculate sample mean and find that it lies in the interval $[0\mathrm{.}30,0\mathrm{.}50]$ with $95\%$ confidance. Calculate population standard derivation from this information. For visual reasons researcher decide to make the confidence interval $[0\mathrm{.}35,0\mathrm{.}45]$ from the same experiment. Can he do this. If so explain how. Otherwise explain how it is impossible for the researchers to narrow down the confidance interval. Take Z$0\mathrm{.}025=1\mathrm{.}96$